exchangeability
On 2010-03-02, at 4:00 AM, r-sig-teaching-request at r-project.org wrote:
I am trying to understand the assumptions for a permutation test and figure out how to explain those to beginning students. (I am working on a project to integrate resampling methods into the first course in statistics.) I have received some help from Tim Hesterberg who gave me the first definition of exchangeability I've seen. One question is whether assumptions apply to randomized experiments or to using permutation tests for survey sampling applications. In addition it would be helpful to have some counterexamples where the assumptions are NOT satisfied (and why).
One perspective is that it makes NO assumptions. It depends what you intend the resulting p-values to mean. If they are to be interpreted as probabilities, then, yes, exchangeability can be seen as an enabling assumption. On the other hand, seen only as a scale of typicality, the randomization/permutation p-values do not *assume* exchangeability so much as provide a test of it. -- Please avoid sending me Word or PowerPoint attachments. See <http://www.gnu.org/philosophy/no-word-attachments.html>